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Proof step 18 from proof cast-add-2pot-h (previous step)

¬(2 ^ i % 2 ^ i = 0 ∧ 0 ≤ 2 ^ i + j ∧ 0 ≤ 2 ^ i ∧ j < 0 ∧ j % 2 ^ i ≠ 0 ∧ 0 < 2 ^ i), 0 ≤ j + 2 ^ (i - 1), 0 < 2 ^ i + j, j < 0, 0 < i, 0 < 2 ^ i + j, (2 ^ i + j) % 2 ^ i < 2 ^ (i - 1) ⊦ cast(i, 2 ^ i + j) = j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
j % 2 ^ i = 0, 0 ≤ j + 2 ^ (i - 1), j < 0, 0 < i, 0 < 2 ^ i + j, (2 ^ i + j) % 2 ^ i < 2 ^ (i - 1) ⊦ cast(i, 2 ^ i + j) = j

Rule argument

Additional information

Used simplifier rules: ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ ¬ 2 ^ i < 0;% ⊦ i < j → ¬ j < i;% ⊦ i + j = j + i;% ⊦ ¬ i ≤ j ↔ j < i;%i ≠ 0 ⊦ i % i = 0;% ⊦ 0 < j → (i ^ j = 0 ↔ i = 0);